In high-dimensional
problems with limited ensemble sizes, we must further
regularize the estimation of the
rearrangements.
In this paper, we introduce a notion of
“localization” for nonlinear updates,
by dropping some variable dependence from each component of the transport map.
We show how sparsity of the KR
rearrangement—a nonlinear function—is linked to properties
of the filtering distribution, such as decay of correlation and (approximate)
conditional independence [1]}.
Intuitively, these sparse transformations
approximate
the projection of the filtering
distribution
onto a manifold of non-Gaussian Markov random fields.
